A Framework for Multi-Site Distributed Simulation and Application to Complex Structural Systems

Accurately assessing the seismic capacity of complex structures requires dynamic testing of full-scale models, including foundations and soil. However, limitations in the size and capacity of existing shaking tables restrict the feasibility of such tests for large structures like bridges or multi-story buildings. Even the largest shaking tables have limitations in size and cost. Pseudo-dynamic (PSD) testing offers an alternative, where inertial and damping forces are analytically computed and applied to the structure, but this approach still faces limitations in experimental site capacity and analysis software capabilities. Different laboratories possess complementary capabilities. For example, UIUC has extensive large-scale structural facilities, while RPI has a high-speed geotechnical centrifuge. Similarly, various analysis platforms have strengths and weaknesses: Zeus-NL excels in collapse analysis, but lacks plate/shell elements, while ABAQUS has diverse element types but limitations in reinforced concrete analysis. OpenSees includes geotechnical models unavailable in other codes. This research addresses these limitations by developing a framework for multi-site testing, multi-code analysis, and hybrid approaches, combining the strengths of different facilities and software.

The literature includes several PSD test algorithms. Implicit time-step integration schemes, using initial stiffness, are common. These include iterative implicit methods using sub-cycling and linearly implicit/nonlinearly explicit operator splitting (OS) methods. A predictor-corrector (PC) algorithm has also been developed, offering improvements over OS methods in the inelastic range. The accuracy and stability of the α-OS method have been extensively studied, highlighting its unconditional stability when initial stiffness is higher than or equal to instantaneous tangent stiffness, its accurate behavior for a specific frequency band with appropriate time steps, and its suitability even with severe stiffness degradation for dominant low-frequency modes.

The proposed framework, UI-SIMCOR, is independent of the integration scheme, allowing for flexibility. Currently, it implements the α-OS method with a modified Newmark scheme. The PC algorithm is under development. UI-SIMCOR uses a distributed architecture where communication between the main control module and sub-structured components is facilitated through the NEESgrid Teleoperation Control Protocol (NTCP). UI-SIMCOR sends commands to apply deformations and collects resulting actions from each module. Each sub-structure can be a physical experimental setup or an analytical model run by a specific software. The framework uses static condensation to reduce the degrees of freedom (DOF). The equation of motion is manipulated to express the system in terms of DOF where masses are defined, DOF of interest, and DOF that can be condensed out. Static condensation eliminates redundant DOF, simplifying the system of equations. The condensed stiffness matrix can be determined from pre-tests or pre-analysis. The main module handles time-step integration; other modules perform static analyses or experiments. The structure can be divided into multiple modules, each with an arbitrary number of DOF. The mass and stiffness matrices are the sums of contributions from all modules. The flowchart describes the implementation of substructure PSD testing. The separation of time-step integration and stiffness calculation allows for versatile combinations of analytical and experimental modules with any number of control points.

The UI-SIMCOR framework, through its separation of time-step integration and stiffness formulation, enables the use of static analysis and testing modules within a distributed simulation environment. This flexibility allows for the integration of diverse analytical platforms and experimental setups. The verification studies demonstrate the successful implementation of this approach in two different scenarios: (1) The Multi-Site Soil-Structure-Foundation Interaction Test (MISST), which combines physical experiment (left pier) and numerical simulation (other piers and deck) to simulate a damaged bridge section. The results show excellent agreement between the hybrid simulation and a model where the whole bridge was simulated as a single structure. (2) A soil-foundation-structure model, where the soil was modeled in OpenSees and the frame in Zeus-NL. The results obtained using substructure PSD simulation matched results from a simulation where the whole system was modeled in OpenSees. These examples validate the framework's ability to handle hybrid simulation and multi-platform analysis efficiently, allowing for optimal use of each platform's strengths. The displacement results from both verification examples exhibit strong correlation between the substructure PSD testing and full-model analyses, demonstrating the accuracy and effectiveness of UI-SIMCOR.

The developed framework successfully addresses the limitations of traditional methods for seismic assessment of complex structures by enabling multi-site distributed simulations. The separation of time-step integration and stiffness calculation is a key innovation, simplifying the implementation and increasing the versatility of the framework. The successful verification tests using both hybrid (MISST) and multi-platform (soil-foundation-structure) simulations highlight the framework's potential for realistic and efficient seismic assessment of complex systems. The results obtained strongly support the framework's accuracy and reliability.

This technical note introduces UI-SIMCOR, a versatile framework for multi-site distributed simulations. The separation of time-step integration and stiffness formulation simplifies implementation and allows for hybrid and multi-platform analysis. Verification examples demonstrate its effectiveness in both hybrid and multi-platform simulations. Future work could investigate the accuracy and stability of the hybrid PSD algorithms in more detail.

While the framework offers significant advantages, future research should focus on further investigation of accuracy and stability, particularly for hybrid simulations involving complex material models and large numbers of substructures. The current implementation relies on pre-tests to determine the condensed stiffness matrices; exploring more efficient methods for obtaining stiffness information online would improve the overall efficiency. The impact of communication latency between distributed modules should be further analyzed and optimized.